As we may know, the periodic or almost periodic phenomena are popular in various
natural problems of real world applications [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}.
In comparing with periodicity, almost periodicity is more
frequent in nature and much more complicated in studying for such model [10]}, [11]}.
On the other hand, many dynamical systems describe the real phenomena depend on the history
as well as undergo abrupt changes in their states. This kind of models are best described by impulsive
delay differential equations [12]}, [13]}, [10]}. A great deal of effort from researchers has been devoted to study the
existence and asymptotic behavior of almost periodic solutions of (REF ) and its generalizations due to
their extensively realistic significance. We refer the reader to [15]}, [16]}, [17]}, [11]}, [19]}, [20]} and the references therein.
Particularly, in [11]}, Wang and Zhang investigated the existence,
nonexistence and uniqueness of positive almost periodic solution of the following model
\(\dot{x}(t)=-a(t)x(t)+\frac{b(t)x(t-\tau (t))}{1+x^n(t-\tau (t))},\quad n>1,\) 
